glasso {glasso}R Documentation

Graphical lasso

Description

Estimates a sparse inverse covariance matrix using a lasso (L1) penalty

Usage

glasso(s, rho, zero=NULL, thr=1.0e-4, maxit=1e4,  approx=FALSE, penalize.diagonal=TRUE, start=c("cold","warm"), w.init=NULL,wi.init=NULL, trace=FALSE)

Arguments

s Covariance matrix:p by p matrix (symmetric)
rho (Non-negative) regularization parameter for lasso. rho=0 means no regularization. Can be a scalar (usual) or a symmetric p by p matrix, or a vector of length p. In the latter case, the penalty matrix has jkth element sqrt(rho[j]*rho[k]).
zero (Optional) indices of entries of inverse covariance to be constrained to be zero. The input should be a matrix with two columns, each row indicating the indices of elements to be constrained to be zero. The solution must be symmetric, so you need only specify one of (j,k) and (k,j). An entry in the zero matrix overrides any entry in the rho matrix for a given element.
thr Threshold for convergence. Default value is 1e-4. Iterations stop when average absolute parameter change is less than thr * ave(abs(offdiag(s)))
maxit Maximum number of iterations of outer loop. Default 10,000
approx Approximation flag: if true, computes Meinhausen-Buhlmann(2006) approximation
penalize.diagonal Should diagonal of inverse covariance be penalized? Dafault TRUE.
start Type of start. Cold start is default. Using Warm start, can provide starting values for w and wi
w.init Optional starting values for estimated covariance matrix (p by p). Only needed when start="warm" is specified
wi.init Optional starting values for estimated inverse covariance matrix (p by p) Only needed when start="warm" is specified
trace Flag for printing out information as iterations proceed. Default FALSE

Details

Estimates a sparse inverse covariance matrix using a lasso (L1) penalty, using the approach of Friedman, Hastie and Tibshirani (2007). The Meinhausen-Buhlmann (2006) approximation is also implemented. The algorithm can also be used to estimate a graph with missing edges, by specifying which edges to omit in the zero argument, and setting rho=0. Or both fixed zeroes for some elements and regularization on the other elements can be specified.

Value

A list with components

w Estimated covariance matrix
wi Estimated inverse covariance matrix
loglik Value of maximized log-likelihodo+penalty
errflag Memory allocation error flag: 0 means no error; !=0 means memory allocation error - no output returned
approx Value of input argument approx
del Change in parameter value at convergence
niter Number of iterations of outer loop used by algorithm

References

Jerome Friedman, Trevor Hastie and Robert Tibshirani (2007). Sparse inverse covariance estimation with the lasso. Biostatistics 2007. http://www-stat.stanford.edu/~tibs/ftp/graph.pdf

Meinshausen, N. and Buhlmann, P.(2006) High dimensional graphs and variable selection with the lasso. Annals of Statistics,34, p1436-1462.

Examples


set.seed(100)

x<-matrix(rnorm(50*20),ncol=20)
s<- var(x)
a<-glasso(s, rho=.01)
aa<-glasso(s,rho=.02, w.init=a$w, wi.init=a$wi)

# example with structural zeros and no regularization,
# from Whittaker's Graphical models book  page xxx.

s=c(10,1,5,4,10,2,6,10,3,10)
S=matrix(0,nrow=4,ncol=4)
S[row(S)>=col(S)]=s
S=(S+t(S))
diag(S)<-10
zero<-matrix(c(1,3,2,4),ncol=2,byrow=TRUE)
a<-glasso(S,0,zero=zero)

[Package glasso version 1.4 Index]